HA, too long time

When everything's properly configured, HA failover causes a small impact which lasts for 1-2 seconds. Most commonly, users just have to re-login after the HA failover and then it's business as usual. A 10-min impact is a clear sign there's a TCP half-closed scenario, incorrect balancing where persistent routing is required or something similar of that nature. Apart from that, you cannot really expect a correct answer to this question as we're not familiar with your implementation of BigIP and application behavior.

You will need to look into persistence and connection mirroring features. As needed, run TCP dump captures on the external and internal vlans to find out what's going on at the lower level. Pair the dump with some application error logs. This will get your started: https://support.f5.com/kb/en-us/solutions/public/13000/400/sol13478.html

First thing I'd look at 10 mins is a long time - Do you have anything on your network which holds a record for 600 seconds ?

It sounds like (And I can't verify) that a switch may not be responding to a gratuitous ARP request when the failover occurs.

When you perform a failover, do the adjacent layer 2 devices update their ARP/MAC tables ?

Thanks for your advice